QuestionSolve $3x + 6y = 24$ and $24 - 3x = 6y$ for $x$ . Also, solve $6y = 24 - 3x$ for $y$ and $24 - 6y = 3r$ for $x$ in terms of $y$ . Find both answers.

Studdy Solution

STEP 1

Assumptions1. The equations are linear equations in two variables, $x$ and $y$ . . The coefficients of $x$ and $y$ are real numbers.
3. The equations are given in the form $ax + by = c$ , $c - ax = by$ , $by = c - ax$ , and $c - by = ax$ respectively.

STEP 2

First, we solve the equation $x +6y =24$ for $x$ . We can do this by subtracting $6y$ from both sides and then dividing by $$.
$x = (24 -6y) /$

STEP 3

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

STEP 4

implify the expression to find $x$ in terms of $y$ .
$x =8 -2y$

STEP 5

Next, we solve the equation $24 -3x =y$ for $x$ . We can do this by subtracting $24$ from both sides, dividing by $-3$ , and then simplifying.
$x = (24 -y) /3$

STEP 6

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

STEP 7

implify the expression to find $x$ in terms of $y$ .
$x = -2y$

STEP 8

Next, we solve the equation $6y =24 -3x$ for $y$ . We can do this by subtracting $24$ from both sides, dividing by $6$ , and then simplifying.
$y = (24 -3x) /6$

STEP 9

Now, plug in the given values to calculate $y$ .
$y = (24 -3x) /6$

STEP 10

implify the expression to find $y$ in terms of $x$ .
$y =4 -0.5x$

STEP 11

Finally, the equation $24 -6y =3x$ does not match the pattern of the other equations. It is not possible to solve this equation for $x$ in terms of $y$ because the variable $r$ is present instead of $x$ .
The "both" answers are $x =8 -y$ and $y =4 -0.5x$ .

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QuestionSolve $3x + 6y = 24$ and $24 - 3x = 6y$ for $x$ . Also, solve $6y = 24 - 3x$ for $y$ and $24 - 6y = 3r$ for $x$ in terms of $y$ . Find both answers.

Studdy Solution

STEP 1

Assumptions1. The equations are linear equations in two variables, $x$ and $y$ . . The coefficients of $x$ and $y$ are real numbers.
3. The equations are given in the form $ax + by = c$ , $c - ax = by$ , $by = c - ax$ , and $c - by = ax$ respectively.

STEP 2

First, we solve the equation $x +6y =24$ for $x$ . We can do this by subtracting $6y$ from both sides and then dividing by $$.
$x = (24 -6y) /$

STEP 3

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

STEP 4

implify the expression to find $x$ in terms of $y$ .
$x =8 -2y$

STEP 5

Next, we solve the equation $24 -3x =y$ for $x$ . We can do this by subtracting $24$ from both sides, dividing by $-3$ , and then simplifying.
$x = (24 -y) /3$

STEP 6

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

STEP 7

implify the expression to find $x$ in terms of $y$ .
$x = -2y$

STEP 8

Next, we solve the equation $6y =24 -3x$ for $y$ . We can do this by subtracting $24$ from both sides, dividing by $6$ , and then simplifying.
$y = (24 -3x) /6$

STEP 9

Now, plug in the given values to calculate $y$ .
$y = (24 -3x) /6$

STEP 10

implify the expression to find $y$ in terms of $x$ .
$y =4 -0.5x$

STEP 11

Finally, the equation $24 -6y =3x$ does not match the pattern of the other equations. It is not possible to solve this equation for $x$ in terms of $y$ because the variable $r$ is present instead of $x$ .
The "both" answers are $x =8 -y$ and $y =4 -0.5x$ .

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QuestionSolve 3x+6y=243x + 6y = 243x+6y=24 and 24−3x=6y24 - 3x = 6y24−3x=6y for xxx. Also, solve 6y=24−3x6y = 24 - 3x6y=24−3x for yyy and 24−6y=3r24 - 6y = 3r24−6y=3r for xxx in terms of yyy. Find both answers.

Studdy Solution

STEP 1

STEP 2

First, we solve the equation x+6y=24x +6y =24x+6y=24 for xxx. We can do this by subtracting 6y6y6y from both sides and then dividing by $$.x=(24−6y)/x = (24 -6y) /x=(24−6y)/

STEP 3

Now, plug in the given values to calculate xxx.x=(24−6y)/3x = (24 -6y) /3x=(24−6y)/3

STEP 4

implify the expression to find xxx in terms of yyy.x=8−2yx =8 -2yx=8−2y

STEP 5

Next, we solve the equation 24−3x=y24 -3x =y24−3x=y for xxx. We can do this by subtracting 242424 from both sides, dividing by −3-3−3, and then simplifying.x=(24−y)/3x = (24 -y) /3x=(24−y)/3

STEP 6

Now, plug in the given values to calculate xxx.x=(24−6y)/3x = (24 -6y) /3x=(24−6y)/3

STEP 7

implify the expression to find xxx in terms of yyy.x=−2yx = -2yx=−2y

STEP 8

Next, we solve the equation 6y=24−3x6y =24 -3x6y=24−3x for yyy. We can do this by subtracting 242424 from both sides, dividing by 666, and then simplifying.y=(24−3x)/6y = (24 -3x) /6y=(24−3x)/6

STEP 9

Now, plug in the given values to calculate yyy.y=(24−3x)/6y = (24 -3x) /6y=(24−3x)/6

STEP 10

implify the expression to find yyy in terms of xxx.y=4−0.5xy =4 -0.5xy=4−0.5x

STEP 11

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QuestionSolve $3x + 6y = 24$ and $24 - 3x = 6y$ for $x$ . Also, solve $6y = 24 - 3x$ for $y$ and $24 - 6y = 3r$ for $x$ in terms of $y$ . Find both answers.

First, we solve the equation $x +6y =24$ for $x$ . We can do this by subtracting $6y$ from both sides and then dividing by $$.
$x = (24 -6y) /$

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

implify the expression to find $x$ in terms of $y$ .
$x =8 -2y$

Next, we solve the equation $24 -3x =y$ for $x$ . We can do this by subtracting $24$ from both sides, dividing by $-3$ , and then simplifying.
$x = (24 -y) /3$

Now, plug in the given values to calculate $x$ .
$x = (24 -6y) /3$

implify the expression to find $x$ in terms of $y$ .
$x = -2y$

Next, we solve the equation $6y =24 -3x$ for $y$ . We can do this by subtracting $24$ from both sides, dividing by $6$ , and then simplifying.
$y = (24 -3x) /6$

Now, plug in the given values to calculate $y$ .
$y = (24 -3x) /6$

implify the expression to find $y$ in terms of $x$ .
$y =4 -0.5x$